An Application of Topologicai Analysis to Studying the Three-Dimensional Flow in Cascades;Part Ⅰ——Topologicai Rules for Skin-Friction Lines and Section Streamlines

Based on the working of Lighthill and Hunt et al., in the present paper the author has established the topological rules adapting to analysing the skin-friction lines and the section streamlines in cascades. These rules are(1) for a rotor cascade without shroud band, the total number of nodal points equals that the saddle points on the skin-friction line vector fields in eachpitch range;(2) for an annular or straight cascade with no-clearances at blade ends, the total number of saddle points is two more than that of nodal points on the skin-friction line fields in a pitch;(3) the total number of saddles in the secondary flow fields on cross-sections in cascade is one less than that of nodes;(4) in the section streamline vector fields on a meridian surface penetrating a flow passage, and on leading and trailing edge sections, the total number of nodes is equal to that of saddles;(5) on the streamline vector fields of a blade-to-blade surface, the total number of nodes is one less than that of saddles.